Question

draw ab= 10cm mark a point c on it such that AC- CB=2 cm​

Answer 1

Solution :-

given that,

→ AB = 10 cm .

C is a point on AB such that, AC - CB = 2 cm .

so,

→ AC - CB = 2 ------ Eqn.(1)

and,

→ AC + CB = AB

→ AC + CB = 10 ------- Eqn.(2)

adding Eqn.(1) and Eqn.(2) we get,

→ (AC - CB) + (AC + CB) = 2 + 10

→ AC + AC - CB + CB = 12

→ 2AC = 12

→ AC = 6 cm .

Putting value of AC in Eqn.(1),

→ 6 - CB = 2

→ CB = 6 - 2

→ CB = 4 cm .

therefore,

→ AC : CB = 6 : 4 = 3 : 2 .

Now, Steps of construction :- (Refer to image.)

• Draw a line segment AB of length 10 cm .
• Draw a ray AX which makes an acute angle with AB .
• Locate (2 + 3) total 5 points A1, A2, A3, A4 and A5 on AX such that AA1 = A1A2 = A2A3 = A3A4 = A4A5 .
• Join A5 to B .
• Through the point A3, draw a line segment which intersects AB at point C and which is parallel to A5B .

Hence, C is our required point on line segment AB now .

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